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Geometry: 3-D Measurements

Volumes of Polyhedra and Spheres

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Problem :
A prism's volume is 24, and its altitude is 3. What is the area of the base of
the prism?

8

Problem :
A sphere of what radius has the same surface area as volume? (With different
units, of course)

A sphere with radius 3 has a surface area of
36Π
square
units, and a volume of
36Π
cubic units.

Problem :
A right pyramid has a square with side length 4 for its base, and an altitude of
7. What is its volume?

112 cubic units

Problem :
A prism has two regular polygons for its bases. Each polygon has apothem 4, and
perimeter 32. The altitude with an endpoint at the center of one polygon has
its other endpoint at a point 6 units away from the center of the other polygon.
The lateral edges of the prism are all of length 10. What is the volume of this
prism?

512 cubic units

Problem :
A circle with diameter 6 forms the base of a cone. What is the volume of this
cone?